Catseye Fractal

I am an avid fan of XaoS and it has a very unique fractal called Catseye. There isn't much documentation on it, I don't know where it came from, and I have no idea what the actual formula looks like. Perhaps it can be uncovered somewhere on GitHub? It has some incredible potential when varying the bailout value and the different fractal planes. Here are some designs I worked up mostly in Julia mode.
Is anyone here familiar with such a formula, is there by chance anything like it in the UF formula database?
The first picture shown is the fractal in raw form as it appears on the XaoS screen.

Thanks in advance for suggestions.

Kathy, nice images. I've seen similar ones made in Paul Carlson's Mind Boggling Fractals program but not in Ultrafractal, which I started using in 1999 or thereabout.

MBF may be available somewhere in the internet, but I don't know if it will run on today's machines. If you do find it, the formulas are given for each fractal type but not for the programming in MBF. It has been a long time since I've used it, but I recall it fondly.

Hope this helps.

Caryn Paris

Thank you, Caryn, for your input. I think it's an amazing formula, whatever it happens to be, and in my eyes it's like a hidden gem because it has so much potential. I just don't know why it seems like a phantom fractal. Other types of formulas are so popular that all the fractal programs have them. I've never tried MBF but the pictures I've seen have very beautiful bright colors. Maybe someday I'll look into it.

I took a quick peek at the XaoS source. It's a bit obscure; it wasn't designed for casual perusing, and I don't have the time to really understand it. But near as I can tell, the formula is:

z = c/z + z/c

I haven't seen anything like it in the UF formula database (but I can't say I'm familiar with all of the thousands of formulas there!). I tried coding it real quick, but my results don't look anything like the ones you posted.

If you want to try it, save the following code to a file named catseye.ufm in your Ultra Fractal formula directory.

Catseye{
;
; Attempt to code the Catseye formula from XaoS.
; The XaoS source credits Arpad Fekete
;
init:
  z = @start
  c = #pixel
loop:
  z = c/z + z/c
bailout:
  |z| <= @bailout
default:
  title = "Catseye"

  param start
    caption = "Starting point"
    default = (0.0, -1.0)
  endparam

  float param bailout
    caption = "Bailout"
    default = 8.0
  endparam

switch:
  type = "CatseyeJulia"
  seed = #pixel
  bailout = bailout
}

CatseyeJulia{
init:
  z = #pixel
  c = @seed
loop:
  z = c/z + z/c
bailout:
  |z| <= @bailout
default:
  title = "Catseye Julia"

  param seed
    caption = "Julia seed"
    default = (0.0,-1.0)
  endparam

  float param bailout
    caption = "Bailout"
    default = 8.0
  endparam

switch:
  type = "Catseye"
  bailout = bailout
}

Greetings. I believe that I've deduced the correct formula from the Xaos source code. I've uploaded Xaos Catseye to the public UF database in folder jam3.ufm; see if that's what you're looking for. You can use the UF switch feature to find useful Julia seeds.
Please let me know if you notice anything unexpected.
Joe

RSidwell - Thank you very much for this, I appreciate your help. Are you by chance on DA under the same name? I'm on there as Kaleidogal. I just commented on a few of your works, beautiful collection! It's nice to find another fractal artist in the States, I'm in PA. Seems so many of the artists are from all over the world, not so many from the United States. The broad scope of fractal art is amazing to me. Thanks again for responding to my post.

Thank you so much, Joe! I'm away from home for a few days and won't be able to try your Catseye formula, but I'm anxious to give it a try. I'll let you know how I make out. Thank you!

Yes, that is me on DA, though I'm not terribly active there. Thanks for your comments. There are certainly amazing fractal artists all over the world, but the U.S. is well represented; I'm sure you'll find more!

Please ignore my formula; I missed a crucial part. I think Joe got it right.

Joe, should I have a checkmark in either of the two boxes labelled Mandelbrot flag and Julia flag? I'm not sure how to use them. Are they necessary when using switch mode? Again, many thanks for the time you spent in converting this formula.

You should never need to manually change the Mandelbrot/Julia checkbox; they are checked automatically according to which mode you are in, using the UF switch feature. I should have made them invisible (and may on a future update). The formula starts out in Mandelbrot mode, and will stay that way until you select Julia coordinates using the switch option; thereafter, you should notice that the checkboxes have been updated automatically.

Got it, thanks.